We have normalized the scale factor so that \(a(t_1) = 1\) .
\(\vec{k}\)  is thus the physical wavevector at time \(t_1\) .
The \(\Phi \)  fluctuations are accompanied by fluctuations in
the temperature [1]}
\({\delta T(\vec{k},t) \over T(t)}&=& ({1 \over 2} + {2 k^2 t t_1 \over 3}) \Phi (\vec{k},t) +{t \over 4} {d \over dt} \Phi (\vec{k},t)\nonumber \\&=& - {3 \over 2} \Phi _p(\vec{k})\cos \left({2 k \sqrt{t t_1 \over 3}}\right)~~~{\rm for}~~~~~ k \sqrt{t t_1} >> 1~~ \ .\) 
